$(40$ points$)$ For the given $M_u$ acting on the section show below do the following

a$.(30$ points$)$ Determine the theoretical steel areas required for the section shown below. The dimensions are limited to the values shown. The distance to the center of the bars on the tension face is $3$ in$.$ If compression steel is required, assume its center will be placed $3$ in$.$ from the compression face $(d^{\text{'}}=3in.).$

b$.(10$ points$)$ Recommend bar sizes and show them on the section below. Be sure to meet the spacing requirements.

$f_c^{\text{'}}=4,000,f_y=60,000,M_U=700$kip$ft$